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Boris Nemtsov's funeral attracted large crowds on Tuesday, two days after a big march in Moscow

Russia's President Vladimir Putin has called for an end to "shameful" political killings in Russia, after the shooting of opposition politician Boris Nemtsov just outside the Kremlin walls.

He said the most serious attention should be paid to high-profile crimes.

The former deputy prime minister, 55, was murdered on Friday night and buried in Moscow on Tuesday.

The motive is unknown, but Mr Putin's aides have rejected suggestions that he had any involvement.

Mr Nemtsov, who had been planning a march against the conflict in eastern Ukraine, said recently that he feared the president would have him killed because of his opposition to the war.

He was shot four times in the back while walking with his Ukrainian girlfriend, Anna Duritskaya, on Great Moskvoretsky Bridge.

At least 50,000 people turned out on Sunday to march in tribute to him.

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The Russian president has vowed to bring the killers to justice

Marchers, some chanting "Russia without Putin", blamed the assassination on a climate of hatred fostered by the Kremlin and its supporters towards opponents of its Ukraine policy.

'Suspects'

"It is necessary to finally rid Russia of the shame and tragedies like the one that we lived through and saw quite recently. I mean the murder, the brazen murder of Boris Nemtsov right in the centre of the capital," Mr Putin said in televised comments to the interior ministry.

After the shooting, which the Kremlin described as a "provocation" aimed at discrediting the president, Mr Putin said he would do all he could to ensure the killers were brought to justice but little progress appears to have been made in the investigation.

When asked by reporters on Tuesday if there were any suspects in the murder, the head of Russia's FSB security service, Alexander Bortnikov, said: "There are always suspects."

Several theories have emerged for who was the behind the murder of a man who was putting together a report on Russia's involvement in eastern Ukraine:

Opposition leader Alexei Navalny said it was either a government or pro-government organisation

Rogue elements in the security services or fighters returning from eastern Ukraine may have wanted to silence his anti-war stance

Or it may have been unrelated to Ukraine: Mr Navalny said it could have been ordered by officials in Yaroslavl, where Mr Nemtsov had been investigating corruption

'Fake'

Russia's finance ministry became part of the story on Tuesday when it was asked about reports that a light-coloured car used by the ministry had been seen in the area at the time of the shooting.

The ministry's press service said the Ford car belonged to an in-house security service, but not the ministry itself, Tass news agency reported.

And Lifenews website, which has close links to the security services, quoted the driver, Dmitry Karmaza, as saying he had driven past the scene a few minutes after the shooting, when a patrol car was already there.

Separately, a video purportedly showing a far-right Russian group active in eastern Ukraine claiming it carried out the killing was dismissed by the group's leader, Alexei Milchakov, as a fake.

"We would have liked to bump him off but we wouldn't even have the money for the car," he wrote earlier on social media.